A tool electrode at the start of a given machining operation or on the occasion of exchanging it for a previous electrode during a given machining operation must be mounted on an electrical machine tool precisely so that it can be positioned in a predetermined alignment or centering relationship with a workpiece or a tool head. Heretofore, this has necessitated repeated loosening and tightening of bolts on a chucking member or device for securing the tool electrode to the tool head or spindle. Indicators must also be employed to measure a deviation in alignment to assist the manual centering correction of the tool electrode relative to predetermined reference surfaces. Such practice has, however, been bothersome to the operator and may not necessarily assure the required centering or alignment correction.